1. Field of the Invention
This invention relates to microscopy and, more particularly, to near-field microscopy wherein an image of an object is directly reconstructed with sub-wavelength resolution.
2. Description of the Background Art
There has been considerable recent interest in the development of near-field methods for optical microscopy. This interest is motivated by the remarkable ability of such methods to image spatial structure with sub-wavelength resolution. It is now well recognized, however, that the analysis and interpretation of near-field images is somewhat problematic. The difficulty can be traced to the fact that the near-field scattered wave is sensitive to variations in both the structure and the dielectric permittivity of the sample under investigation. As a consequence, the connection between the image and the structure of the sample is unclear, with the implication that different samples may give rise to the same image. For this reason there is substantial interest in the near-field inverse scattering problem. To date, work in this direction has been limited to the study of the inverse problem for homogeneous media.
Representative of the art in this technological area are the following U.S. Patents: (a) Fiber Optic Probe for Near Field Optical Microscopy (U.S. Pat. No. 5,485,536); (b) Method and Apparatus for Performing Near-Field Optical Microscopy (U.S. Pat. No. 5,479,024); (c) Near Field Scanning Tunneling Optical Microscope (U.S. Pat. No. 5,382,789; and (d) Near Field Optical Microscopic Examination of a Biological Specimen (U.S. Pat. No. 5,286,970).
The art is devoid of any teachings or suggestions for treating the inverse scattering procedure which is applicable to the near-field case.
These shortcomings, as well as other limitations and deficiencies, are obviated, in accordance with the present invention, by devising explicit inversion formulas and obtaining from the observation that it is possible to construct the singular value decomposition of the high-frequency part of the scattering operator. This approach provides considerable insight into the mathematical structure of the inverse problem and allows the separation of effects due to structure and permittivity.
The scattering problem for scalar waves in the near field is treated herein. An analytic solution to this problem is presented in the form of an explicit inversion formula which are applicable to near-field optical microscopy.
In accordance with a broad method aspect of the present invention, an image of an object is generated by: (a) probing the object with a source of waves; (b) detecting scattered waves from the object; and (c) directly reconstructing the image by executing a prescribed mathematical algorithm on the scattered waves which generates the image with sub-wavelength spatial resolution.